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Abstract

In microscopy, single fluorescence point sources can be localized with a precision several times greater than the resolution limit of the microscope. We show that the intermittent fluorescence or ‘blinking’ of quantum dots can analyzed by an Independent Component Analysis so as to identify the light emitted by each individual nanoparticle, localize it precisely, and thereby resolve groups of closely spaced (< λ/30) quantum dots. Both simulated and experimental data demonstrate that this technique is superior to localization based on Maximum Likelihood Estimation of the sum image under the assumption of point emitters. This technique has general application to any emitter with non-Gaussian temporal intensity distribution, including triplet state blinking. When applied to the labeling of structures, a high resolution “image” consisting of individually localized points may be reconstructed leading to the term “Pointillism”.

Figures (3)

Ability of the ICA approach to localize two blinking sources compared to fitting the sum image to a 2 source model with a maximum likelihood estimate. Each point represents the average of 50 simulations. To account for outliers (found only in the MLE analysis), localization errors > 4 pixels were ignored. The photon counts refer to the expected maximum photons per dot per image. Each pixel corresponded to 108 nm as given by the geometry of the experiments. The black line indicates where the localization error was equal to the separation. (a) The mean localization error divided by separation (b) 1000 expected max photons as for one of the above cases but with the data series and the PSF smoothed (Gaussian kernel with indicated width σ) in x and y before analysis. A smoothing with σ = 1 pixel leads to a beneficial trade off between signal to noise and spatial resolution.

The results of the ICA decomposition for three examples of experimentally acquired blinking QD data sets. Top: 10 frames from the time series. Bottom, left to right: Sum image of time series, ICA returned component 1, ICA returned component 2, color overlay of component 1 and 2. Images are 32×32 pixels with pixel size of 108 nm. (a) Two widely separated blinking quantum dots, separation distance is found to be 435 nm. (b) Two closely spaced QDs, separation is found to be 23 nm. (c) Only a single quantum dot is found, the other component is noise.

The results of the ICA decomposition of 3 blinking emitters. The coordinates in pixels with respect to the center of the image are (0.9501,-0.2311), (1.3380,-0.5467) and (0.9881,-0.7297). The data series was simulated with 1000 photons per dot per QD and 500 time frames. Images are 16×16 pixels with a pixel size of 108 nm. (a and b) are the images found when the ICA analysis assumes 2 emitters. Localization yields coordinates of (0.9801,-0.2139) and (1.1497,-0.6448). (c, d, and e) are the images found when the ICA analysis assumes 3 emitters. Localization yields coordinates (1.0024,-0.7596),(1.3447,-0.5623) and (0.9553,-0.2648). (d, e, f and g) are the images found when the ICA analysis assumes 4 emitters. Localization yields coordinates of (1.3397 -0.5558),(0.9487 -0.2636),(0.0485 0.2060), and (0.9897 -0.7659).